Bending, free vibration, and buckling of modified couples stress-based functionally graded porous micro-plates

The study using numerical methods on porous functionally graded (FG) nanoplates is still somewhat limited. This paper focuses on porosity-dependent nonlinear transient analysis of FG nanoplates using isogeometric finite element approach. In order to capture the small size effects, the Eringen's nonlocal elasticity based on higher order shear deformation theory (HSDT) are used to model the porous FG nanoplates. Two distributions of porosities inside FG materials are incorporated and defined via a modified rule of mixture. The nonlinear transient nonlocal governing equations under transverse dynamic loads are formulated by using the von Karman strains and are solved by Newmark time integration scheme to obtain geometrically nonlinear responses. It is indicated that nonlinear transient deflections of the porous FG nanoplate are significantly influenced by material composition, porosity, nonlocal parameters, volume fraction exponent, porosity distributions, geometrical parameters and dynamic load characteristics.

Porosity-dependent nonlinear transient responses of functionally graded nanoplates using isogeometric analysis

https://northumbria-test.eprints-hosting.org/id/document/269061

Isogeometric analysis for size-dependent nonlinear thermal stability of porous FG microplates

A quasi-3D refined theory for functionally graded single-layered and sandwich plates with porosities

The nonlinear forced vibrations of functionally graded material (FGM) sandwich cylindrical shells with porosities on an elastic substrate are studied. A step function and a porosity volume fraction are introduced to describe the porosities in FGM layers of sandwich shells. Using the Donnell’s nonlinear shallow shell theory and Hamilton’s principle, an energy approach is employed to gain the nonlinear equations of motion. Afterwards, the multi-degree-of-freedom nonlinear ordinary differential equations are carried out by using Galerkin scheme, and subsequently the pseudo-arclength continuation method is utilized to perform the bifurcation analysis. Finally, the effects of the core-to-thickness ratio, porosity volume fraction, power-law exponent, and external excitation on nonlinear forced vibration characteristics of FGM sandwich shells with porosities are investigated in detail.

Nonlinear forced vibrations of FGM sandwich cylindrical shells with porosities on an elastic substrate

Nonlinear thermomechanical buckling and post-buckling response of porous FGM plates using Reddy's HSDT

In this paper, the first-order shear deformation theory is used to derive theoretical formulations illustrating the nonlinear dynamic response of functionally graded porous plates under thermal and mechanical loadings supported by Pasternak’s model of the elastic foundation. Two types of porosity including evenly distributed porosities (Porosity-I) and unevenly distributed porosities (Porosity-II) are assumed as effective properties of FGM plates such as Young’s modulus, the coefficient of thermal expansion, and density. The strain-displacement formulations using Von Karman geometrical nonlinearity and general Hooke’s law are used to obtain constitutive relations. Airy stress functions with full motion equations which is employed to shorten the number of governing equations along with the boundary and initial conditions lead to a system of differential equations of the nonlinear dynamic response of porous FGM plates. Considering linear parts of these equations, natural frequencies of porous FGM plates are determined. By employing Runge-Kutta method, the numerical results illustrate the influence of geometrical configurations, volume faction index, porosity, elastic foundations, and mechanical as well as thermal loads on the nonlinear dynamic response of the plates. Good agreements are obtained in comparison with other results in the literature.

https://jacm.scu.ac.ir/article_13360_3116a49d3d02a64431d8d692fd83c1e3.pdf

Trinh Minh Chien

Papers

Nonlinear thermomechanical buckling and post-buckling response of porous FGM plates using Reddy's HSDT

Nonlinear Dynamic Response of Functionally Graded Porous Plates on Elastic Foundation Subjected to Thermal and Mechanical Loads